Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.adox)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=11/4, b_1`>=-11/2

For fixed z and a₁=11/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.adox.01

Input Form

HypergeometricPFQ[{11/4}, {-(11/2), -(15/4)}, -z] == (1/(756392175 z^(1/4))) (Sqrt[2] ((756392175 + 1411932060 z + 317837520 z^2 - 280748160 z^3 + 70076160 z^4 + 2838528 z^5 + 38338560 z^6 - 1048576 z^7) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (252130725 + 134469720 z - 137380320 z^2 + 39916800 z^3 - 7096320 z^4 + 3571712 z^5 + 2097152 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (756392175 - 605113740 z + 202577760 z^2 - 43243200 z^3 + 10644480 z^4 - 5062656 z^5 + 262144 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]